Quantifying the information content of surface plasmon resonance reflection spectra

Abstract

Thin-film sensors based on the principle of surface plasmon resonance (SPR) are often used for real-time refractometry of dielectric and metal thin films. We present mathematical methods based on linear estimation which allow quantitative investigation of the capabilities of the SPR technique relative to an ideal thin-film sensor. These methods use a linear model of the sensor response to determine the best possible uncertainty of film parameters extracted from a given set of measurements. These methods are general in that they may be easily applied to any well-modeled system. We show how these methods may be used to quantify the limitations of the basic SPR technique (in particular, the difficulty of determining the thickness and refractive index of a thin film independently) and also to evaluate the capabilities of more elaborate SPR-based techniques designed to overcome these limitations. As an example, we analyze a two-color SPR technique proposed by Peterlinz and Georgiadis and find that the uncertainty of the thickness and refractive index estimates yielded by this technique have a complex dependence on the dispersion of the thin film and its surrounding solvent.